From a30a07a6f985aa15ee8c1558f323ace7ae042671 Mon Sep 17 00:00:00 2001 From: Matthias Clasen Date: Sun, 6 Dec 2020 20:54:30 -0500 Subject: [PATCH] Add gsk_curve_get_tight_bounds Add a way to get a tight bounding box for the various types of curves we use. This will be used in finding intersections. --- gsk/gskcurve.c | 170 +++++++++++++++++++++++++++++++++++++++++- gsk/gskcurveprivate.h | 3 +- 2 files changed, 168 insertions(+), 5 deletions(-) diff --git a/gsk/gskcurve.c b/gsk/gskcurve.c index 81a051c833..41723311d9 100644 --- a/gsk/gskcurve.c +++ b/gsk/gskcurve.c @@ -48,6 +48,8 @@ struct _GskCurveClass graphene_vec2_t *tangent); void (* get_end_tangent) (const GskCurve *curve, graphene_vec2_t *tangent); + void (* get_tight_bounds) (const GskCurve *curve, + graphene_rect_t *bounds); }; /** LINE **/ @@ -161,6 +163,16 @@ gsk_line_curve_get_tangent (const GskCurve *curve, return get_tangent (&self->points[0], &self->points[1], tangent); } +static void +gsk_line_curve_get_bounds (const GskCurve *curve, + graphene_rect_t *bounds) +{ + const GskLineCurve *self = &curve->line; + + graphene_rect_init (bounds, self->points[0].x, self->points[0].y, 0, 0); + graphene_rect_expand (bounds, &self->points[1], bounds); +} + static const GskCurveClass GSK_LINE_CURVE_CLASS = { gsk_line_curve_init, gsk_line_curve_eval, @@ -170,7 +182,8 @@ static const GskCurveClass GSK_LINE_CURVE_CLASS = { gsk_line_curve_get_start_point, gsk_line_curve_get_end_point, gsk_line_curve_get_tangent, - gsk_line_curve_get_tangent + gsk_line_curve_get_tangent, + gsk_line_curve_get_bounds }; /** CURVE **/ @@ -183,7 +196,7 @@ gsk_curve_curve_init_from_points (GskCurveCurve *self, self->has_coefficients = FALSE; memcpy (self->points, pts, sizeof (graphene_point_t) * 4); } - + static void gsk_curve_curve_init (GskCurve *curve, gskpathop op) @@ -353,6 +366,80 @@ gsk_curve_curve_get_end_tangent (const GskCurve *curve, return get_tangent (&self->points[2], &self->points[3], tangent); } +static inline gboolean +acceptable (float t) +{ + return 0 <= t && t <= 1; +} + +/* Solve P' = 0 where P is + * P = (1-t)^3*pa + 3*t*(1-t)^2*pb + 3*t^2*(1-t)*pc + t^3*pd + */ +static int +get_cubic_extrema (float pa, float pb, float pc, float pd, float t[2]) +{ + float a, b, c; + float d, tt; + int n = 0; + + a = 3 * (pd - 3*pc + 3*pb - pa); + b = 6 * (pc - 2*pb + pa); + c = 3 * (pb - pa); + + if (fabs (a) > 0.0001) + { + if (b*b > 4*a*c) + { + d = sqrt (b*b - 4*a*c); + tt = (-b + d)/(2*a); + if (acceptable (tt)) + t[n++] = tt; + tt = (-b - d)/(2*a); + if (acceptable (tt)) + t[n++] = tt; + } + else + { + tt = -b / (2*a); + if (acceptable (tt)) + t[n++] = tt; + } + } + else if (fabs (b) > 0.0001) + { + tt = -c / b; + if (acceptable (tt)) + t[n++] = tt; + } + + return n; +} + +static void +gsk_curve_curve_get_tight_bounds (const GskCurve *curve, + graphene_rect_t *bounds) +{ + const GskCurveCurve *self = &curve->curve; + const graphene_point_t *pts = self->points; + float t[4]; + int n; + + graphene_rect_init (bounds, pts[0].x, pts[0].y, 0, 0); + graphene_rect_expand (bounds, &pts[3], bounds); + + n = 0; + n += get_cubic_extrema (pts[0].x, pts[1].x, pts[2].x, pts[3].x, &t[n]); + n += get_cubic_extrema (pts[0].y, pts[1].y, pts[2].y, pts[3].y, &t[n]); + + for (int i = 0; i < n; i++) + { + graphene_point_t p; + + gsk_curve_curve_eval (curve, t[i], &p, NULL); + graphene_rect_expand (bounds, &p, bounds); + } +} + static const GskCurveClass GSK_CURVE_CURVE_CLASS = { gsk_curve_curve_init, gsk_curve_curve_eval, @@ -362,7 +449,8 @@ static const GskCurveClass GSK_CURVE_CURVE_CLASS = { gsk_curve_curve_get_start_point, gsk_curve_curve_get_end_point, gsk_curve_curve_get_start_tangent, - gsk_curve_curve_get_end_tangent + gsk_curve_curve_get_end_tangent, + gsk_curve_curve_get_tight_bounds }; /** CONIC **/ @@ -686,6 +774,72 @@ gsk_conic_curve_get_end_tangent (const GskCurve *curve, return get_tangent (&self->points[1], &self->points[3], tangent); } +/* Solve N = 0 where N is the numerator of (P/Q)', with + * P = (1-t)^2*a + 2*t*(1-t)*w*b + t^2*c + * Q = (1-t)^2 + 2*t*(1-t)*w + t^2 + */ +static int +get_conic_extrema (float a, float b, float c, float w, float t[4]) +{ + float q, tt; + int n = 0; + float w2 = w*w; + float wac = (w - 1)*(a - c); + + if (wac != 0) + { + q = - sqrt (a*a - 4*a*b*w2 + 4*a*c*w2 - 2*a*c + 4*b*b*w2 - 4*b*c*w2 + c*c); + + tt = (- q + 2*a*w - a - 2*b*w + c)/(2*wac); + + if (acceptable (tt)) + t[n++] = tt; + + tt = (q + 2*a*w - a - 2*b*w + c)/(2*wac); + + if (acceptable (tt)) + t[n++] = tt; + } + + if (w * (b - c) != 0 && a == c) + t[n++] = 0.5; + + if (w == 1 && a - 2*b + c != 0) + { + tt = (a - b) / (a - 2*b + c); + if (acceptable (tt)) + t[n++] = tt; + } + + return n; +} + +static void +gsk_conic_curve_get_tight_bounds (const GskCurve *curve, + graphene_rect_t *bounds) +{ + const GskConicCurve *self = &curve->conic; + float w = gsk_conic_curve_get_weight (self); + const graphene_point_t *pts = self->points; + float t[8]; + int n; + + graphene_rect_init (bounds, pts[0].x, pts[0].y, 0, 0); + graphene_rect_expand (bounds, &pts[3], bounds); + + n = 0; + n += get_conic_extrema (pts[0].x, pts[1].x, pts[3].x, w, &t[n]); + n += get_conic_extrema (pts[0].y, pts[1].y, pts[3].y, w, &t[n]); + + for (int i = 0; i < n; i++) + { + graphene_point_t p; + + gsk_conic_curve_eval (curve, t[i], &p, NULL); + graphene_rect_expand (bounds, &p, bounds); + } +} + static const GskCurveClass GSK_CONIC_CURVE_CLASS = { gsk_conic_curve_init, gsk_conic_curve_eval, @@ -695,7 +849,8 @@ static const GskCurveClass GSK_CONIC_CURVE_CLASS = { gsk_conic_curve_get_start_point, gsk_conic_curve_get_end_point, gsk_conic_curve_get_start_tangent, - gsk_conic_curve_get_end_tangent + gsk_conic_curve_get_end_tangent, + gsk_conic_curve_get_tight_bounds }; /** API **/ @@ -780,3 +935,10 @@ gsk_curve_get_end_tangent (const GskCurve *curve, { get_class (curve->op)->get_end_tangent (curve, tangent); } + +void +gsk_curve_get_tight_bounds (const GskCurve *curve, + graphene_rect_t *bounds) +{ + get_class (curve->op)->get_tight_bounds (curve, bounds); +} diff --git a/gsk/gskcurveprivate.h b/gsk/gskcurveprivate.h index 0f4e89d2c5..a64e8ce736 100644 --- a/gsk/gskcurveprivate.h +++ b/gsk/gskcurveprivate.h @@ -103,7 +103,8 @@ void gsk_curve_get_start_tangent (const GskCurve void gsk_curve_get_end_tangent (const GskCurve *curve, graphene_vec2_t *tangent); - +void gsk_curve_get_tight_bounds (const GskCurve *curve, + graphene_rect_t *bounds); G_END_DECLS